Extraordinary large heat current rectification in a hybrid thermal diode M. J. Mart´ ınez-P´ erez, ∗ A. Fornieri, and F. Giazotto † NEST, Istituto Nanoscienze-CNR and Scuola Normale Superiore, I-56127 Pisa, Italy We report the realization of an ultra-efficient low-temperature hybrid heat current rectifier, thermal counter- part of the well-known electric diode. Our design is based on a tunnel junction between two different elements: a normal metal and a superconducting island. Electronic heat current asymmetry in the structure arises from large mismatch between the thermal properties of these two. We demonstrate experimentally temperature differences exceeding 60 mK between the forward and reverse thermal bias configurations. Our device offers a remark- ably large heat rectification ratio up to ∼ 140 and allows its prompt implementation in true solid-state thermal nanocircuits and general-purpose electronic applications requiring energy harvesting or thermal management and isolation at the nanoscale. Thermal diodes [1–3], i.e., devices allowing heat to flow preferentially in one direction, constitute one of the key tools for the implementation and development of solid-state ther- mal circuits. These would find immediate application in many fields of nanoscience in which energy plays a crucial role [4– 6], e.g., cooling, energy harvesting, thermal isolation, ultra- sensitive cryogenic radiation detection [6], quantum informa- tion [7], or emerging fields such as nanophononics [8], ther- mal logic [1] and coherent caloritronics [9–11]. Yet, both in terms of electronic [12, 13] or phononic heat conduction [14, 15], the experimental realization of thermal diodes re- mains still very challenging [16]. A highly-efficient thermal diode should provide differences of at least one order of magnitude between the total heat cur- rent transmitted in the forward temperature bias configura- tion, J fw , and that generated upon temperature bias rever- sal, J rev . In other words, a thermal rectification coefficient R = J fw /J rev ≫ 1 or ≪ 1 is required. So far, R ∼ 1.07 − 1.4 has been reported in devices where thermal transport occurred thanks to lattice phonons [17–19]. In the context of heat con- duction by electrons, which is the scope of the present work, R ∼ 1.1 was obtained with a quantum-dot thermal rectifier at cryogenic temperatures [20]. Here we show that unprece- dented thermal rectification ratios reaching ∼ 140 can be at- tained in a hybrid device combining normal metals tunnel- coupled to superconductors [21, 22]. Our approach provides with a world-beater experimental realization of a thermal diode, ready to be put into use in low-temperature solid-state thermal circuits. Our thermal diode has been experimentally implemented by means of a NIS junction, where N stands for a normal metal, I for a thin insulating layer and S denotes a supercon- ductor. As schematized in Fig. 1A, the diode operates in- serted between two identical right and left N reservoirs. As we will demonstrate, large directional thermal flux mismatch results from asymmetrical coupling with both right and left electrodes as well as from asymmetrical heat exchange with the thermal bath. The device has been fabricated by electron beam lithogra- phy, three-angle shadow mask evaporation of metals and in- situ oxidation [23]. The diode’s core, enlarged in the top part of Fig. 1B, consists of a NIS junction including two normal metal probes, P N and P S , tunnel-coupled to both the N and S electrodes, respectively. These probes are used for prelimi- nary electrical characterizations. As it will be discussed later, P N is also essential for enhancing the efficiency of the diode. The full device, shown in the bottom part of Fig. 1B, is tunnel- connected to two right and left normal metal electrodes that constitute the thermal reservoirs and are used for investigating the thermal properties of the diode. To this end, they include four tunnel-coupled superconducting wires operating either as heaters or thermometers [6, 9, 10]. Aluminum (Al) with criti- cal temperature ≈ 1.5 K implements all superconducting parts of the structure whereas Al 0.98 Mn 0.02 has been used as a nor- mal metal [24]. Measurements have been performed down to 50 mK of bath temperature (T bath ) in a dilution refrigerator. Despite its intrinsic asymmetry, our device is fully symmet- ric from the electrical side. This is confirmed by the differen- tial conductance (G = ∂ I /∂ V ) obtained from the experimen- tal current (I ) vs. voltage ( V ) characteristic shown in Fig. 1C. Electrical conductance measurements are performed through the series connection of two superconducting probes attached to the right and left reservoirs. This leads to a total resis- tance 1/G ∼ 50 kΩ for bias voltage well above 4Δ 0 /e, where Δ 0 ≈ 230 μ eV is the zero-temperature superconducting en- ergy gap of Al, and e is the electron charge. Directional thermal current mismatch is demonstrated by imposing an electronic temperature gradient across the de- vice. This is possible since electrons in metallic thin films are weakly coupled to lattice phonons at sub-kelvin tempera- tures [6]. As a consequence, each subsystem of the structure can be described by a Fermi-like energy distribution charac- terized by its own electronic temperature that can largely dif- fer from that of the phonon bath [25]. In the forward con- figuration, the bias temperature on the left electrode (T bias ) is intentionally raised above T bath by injecting a power J heater while monitoring the resulting electronic temperature on the right reservoir (T fw ). The measurement procedure is inverted in the reverse configuration, in which the temperature on the left lead (T rev ) is probed for an increasing T bias set in the right electrode. Three representative curves, obtained at different T bath , are shown in Fig. 2A. Differences between the tem- peratures measured in the forward (full symbols) and reverse configurations (open symbols) reveal, at a first glance, large thermal asymmetry which becomes more evident by lower- ing T bath . Furthermore, the intersection between T fw and T rev , arXiv:1403.3052v1 [cond-mat.mes-hall] 12 Mar 2014